Answers
Given that,
Modulus of vector A=4.00
The angle made by the vector A with the y axis, θ₁=33.0°
The modulus of vector B=3.20 m
The angle made by the vector B with the x-axis is θ₂=40.0+90.0=130°
The modulus of the vector C=2.70 m
The angle made by the vector C with x-axis θ₃=-90°
The x and y components of the vector can be written as
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]Where r is the magnitude (or modulus) of the vector and θ is the angle made by the vector.
Or a vector, in cartesian coordinates, can be written as,
[tex]R=r\cos \theta\hat{\text{i}}+r\sin \theta\hat{j}[/tex]Therefore, vector A is cartesian coordinates is
[tex]\begin{gathered} \vec{A}=4.00\cos 33^{\circ}\hat{i}+4.00\sin 33.0^{\circ}\hat{j} \\ =3.35\hat{i}+2.18\hat{j} \end{gathered}[/tex]And the vector B is
[tex]\begin{gathered} \vec{B}=3.20\cos (130^{\circ})\hat{i}+3.20\sin (130^{\circ})\hat{j} \\ =-2.06\hat{i}+2.45\hat{j} \end{gathered}[/tex]And vector C is given by,
[tex]\begin{gathered} \vec{C}=2.70\cos (-90^{\circ})\hat{i}+2.70\sin (-90^{\circ})\hat{j} \\ =-2.7\hat{j} \end{gathered}[/tex]The given equation is
[tex]2.00\vec{A}-\vec{B}+1.30\vec{C}[/tex]Let this represents a vector V
On substituting the known values,
[tex]\begin{gathered} \vec{V}=2.00\vec{A}-\vec{B}+1.30\vec{C} \\ =2.00\times(3.35\hat{i}+2.18\hat{j})-(-2.06\hat{i}+2.45\hat{j)}+1.30(-2.7\hat{j}) \\ =8.76\hat{i}-1.6\hat{j} \end{gathered}[/tex](a) This is the representation with the unit vectors, where i and j are the unit vectors along the x-axis and y-axis respectively.
[tex]\vec{V}=8.76\hat{i}-1.6\hat{j}[/tex]b) The modulus of any vector is the square root of the sum of the squares of its components.
That is, the magnitude of the vector V is
[tex]\begin{gathered} V=\sqrt[]{8.76^2+(-1.6)^2} \\ =8.90\text{ m} \end{gathered}[/tex]The angle of this vector with the x-axis is given by
[tex]\begin{gathered} \phi=\tan ^{-1}(\frac{-1.6}{8.75}) \\ =-10.36^{\circ}^{} \end{gathered}[/tex]The negative sign indicates that the vector is below the positive x-axis
Therefore the modulus of the resultant of the above equation is 8.90 m and its angle with the positive x-axis is -10.36°
Related Questions
What is the average velocity of a car that travels 48 km north in 2.0 h?
Answers
The average velocity of the car would be 24 kilometers per hour in the north direction if the car travels 48 kilometers in the north for 2 hours.
What is Velocity?The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.
As given in the problem, we have to find the average velocity of the car if the car travels 48 kilometers in the north for 2 hours.
The average velocity of the car = 48 kilometers / 2 hours
= 24 kilometers per hour
Thus, the average velocity of the car would be 24 kilometers per hour
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The heating element of an iron operates at 110 V with a current of 11 A.(a) What is the resistance of the iron? Ω(b) What is the power dissipated by the iron? W
Answers
(a)
In order to calculate the resistance, we can use Ohm's Law:
[tex]\begin{gathered} R=\frac{V}{I}\\ \\ R=\frac{110}{11}\\ \\ R=10\text{ \Omega} \end{gathered}[/tex](b)
To calculate the power, we can use the formula below:
[tex]\begin{gathered} P=I\cdot V\\ \\ P=11\cdot110\\ \\ P=1210\text{ W} \end{gathered}[/tex]A/An _____ is described as a device that is used to measure potential difference across any part of a circuit.ammeterfuseground fault interruptervoltmeter
Answers
Answer:
[tex]\text{Voltmeter}[/tex]Explanation: We need to find an instrument that measures potential difference across any part of the circuit, a potential difference is basically voltage difference across a circuit difference and the device used to measure this difference is known as:
[tex]\text{ Voltmeter}[/tex]Voltmeter used in a circuit
The couple required to hold a triple turn of 1.5cm² area in equilibrium when carrying a current 2A at 70° to a field with 0.15T is?
Answers
The couple or torque required to hold the triple turn is 1.27 x 10⁻⁴ Nm.
What is the couple or torque required?
The couple required to hold the triple turn is calculated as follows;
τ = M x Bsinθ
where;
M is the magnetic moment B is the magnetic field strengthThe magnetic moment is calculated as follows;
M = NIA
where;
N is number of turns = 3I is current = 2 AA is the area of the loop = 1.5 cm² = 0.00015 m²M = (3) x (2) x (0.00015)
M = 0.0009 m²A
The torque or couple required is calculated as;
τ = (0.0009) x (0.15 x sin70)
τ = 1.27 x 10⁻⁴ Nm
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Below is a diagram of a 5.0 kg block being dragged to the right, along a horizontal surface. The
coefficient of dynamic friction, is 0.40. Take acceleration due to gravity, g, as 9.81 ms ².
5 kg
30. N
What is the acceleration of the block? Give your answer correct to two significant figures, in
m-s-2, without units.
Answers
The acceleration of the block when the coefficient of friction is 0.40 is 3.924 m/s².
The ratio of the frictional resistive force to the perpendicular force pushing the objects together is known as the coefficient of friction.
Acceleration is the rate at which an object's velocity with respect to time changes.
The block of mass 5 kg is dragged to the right on a horizontal surface.
The coefficient of friction is 0.40.
The acceleration due to gravity is 9.81 m/s².
The force on the block is 30 N.
Now, the force is defined as the product of the mass and acceleration of the object.
Now, using the conservation of force:
F = μmg
ma = μmg
a = μg
a = 0.40 × 9.81
a = 3.924 m/s²
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Your engineering team has created a 46.9 kg spider robot that moves along a strand of web for
Halloween. The spider begins at rest and moves straight down the strand increasing its speed
at a constant rate. It covers 3.04 m in a time of 6.08 s. What is the Tension, in Newtons, in
the strand of web?
Answers
The fabric of the spiderwebs is so thin that it adheres easily to the hook side of a Velcro strip. Push Velcro onto the object you want to attach your webs to, then remove the adhesive backing. Grab a few of the strands and put them onto the Velcro to keep the webs in place.
Explain about the web for Halloween?A black spider spread between two slices of buttered bread is said to offer a witch great power. Spiders were rumoured to help witches cast charms. Old customs claim that if you see a spider on Halloween, the ghost of a departed loved one is purportedly watching over you.
The spiderwebs stick in the hook side of a Velcro strip with ease because they are constructed of a very thin fabric. When you wish to attach your webs to something, push Velcro onto the surface and peel off the sticky backing. To ensure that the webs stay in place, grab a handful of the strands and push them onto the Velcro.
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The velocity-time table represents the motion of a rightward-
moving motorcycle.
Magnitude =
Time (s)
0.0
0.5
1.0
1.5
2.0
What is the magnitude (i.e., value) and direction of the
acceleration?
Direction =
Velocity (m/s)
24.0, right
22.0, right
20.0, right
18.0, right
16.0, right
m/s/s
(No -
sign.)
(Tap field to change.)
NE
Answers
The direction of motion of a body or object depends on its velocity. Speed can be thought of as a scalar quantity in its simplest form. In essence, velocity is a vector quantity. It is the speed at which distance is changing.
What is velocity?Galileo Galilei, an Italian physicist, is credited with being the first to calculate speed by dividing it by the required amount of time and the distance traveled.
Speed, according to Galileo, is the distance traveled in a set amount of time.
The speed at which an object is moving is referred to as its velocity.
Examples of fast motion include an automobile driving north on a highway or a rocket blasting off.
The equation v = u + at, where v signifies the ultimate speed, can be used to express an object's final velocity, which is equal to its starting velocity plus acceleration times the distance traveled.
Therefore, the direction of motion of a body or object depends on its velocity. Speed can be thought of as a scalar quantity in its simplest form. In essence, velocity is a vector quantity. It is the speed at which distance is changing.
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Hafthor bjornson broke the deadlift record in April 2020, lifting 501kg. A) How much weight (in N) did he lift?B) How hard was the floor pushing up on the weights when they were on the floor?
Answers
Given, the mass that Hafthor Bjornson lifted, m=501 kg
A)
The weight is given by the product of the mass and the acceleration due to gravity.
Thus the weight lifted by him is,
[tex]\begin{gathered} W=mg \\ =501\times9.8 \\ =4909.8\text{ N} \end{gathered}[/tex]Thus the weight he lifted is 4909.8 N
B)
When the weight is on the floor the force applied by the floor on the weights is equal to the weight itself. This force is called the normal force.
Thus the force applied by the floor on the weights is 4909.8 N
What is the volume of a piece of iron ( = 7.9 g/cm3) that has a mass of 0.75 kg? (Enter your answer in cm3.) answer in: cm3
Answers
We will have the following:
[tex]\begin{gathered} \frac{7.9g}{cm^3}\ast\frac{1kg}{1000g}=\frac{0.75kg}{V}\Rightarrow0.0079kg/cm^3=\frac{0.75kg}{V} \\ \\ \Rightarrow V=\frac{0.75kg}{0.0079kg/cm^3}\Rightarrow V=\frac{7500}{79}cm^3 \\ \\ \Rightarrow V\approx94.9cm^3 \end{gathered}[/tex]So, the volume is 7500/79 cm^3, that is approximately 94.9 cm^3.
Projections of a vector make up the components of that vector. Is this true or false?
Answers
The given statement 'Projections of a vector make up the components of that vector' is true. The direction of a vector
find the pressure increase in a fluid when a force of 25 N is exerted on a closed syringe where the piston radius is 2 cm.
Answers
Given:
• Force, F = 25 N
,• Radius, r = 2 cm
Let's find the pressure increase.
To find the pressure increase, apply the formula:
[tex]\Delta P=\frac{Force}{Area}=\frac{F}{\pi r^2}[/tex]Where:
F = 25 N
r is the radius in meters = 2 cm
P is the pressure
Convert the radius from cm to meters.
Where:
100 cm = 1 m
2 cm = 2 /100 = 0.02 m
Hence, we have:
[tex]\begin{gathered} \Delta P=\frac{25}{\pi(0.02)^2} \\ \\ \Delta P=\frac{25}{\pi(0.0004)} \\ \\ \Delta P=\frac{25}{0.00125664} \\ \\ \Delta P=19894.4\text{ Pa}\approx1.99\times10^4\text{ Pa} \end{gathered}[/tex]Therefore, the pressure increase is 1.99 x 10⁴ Pa.
ANSWER:
1.99 x 10⁴ Pa
Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s. The waves have the same amplitude. The drawing shows the position of the waves at time t = 0 s. Which one of the following drawings depicts the waves on the rope at t = 4.0 s?
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We know the graph when t = 0. Therefore, at t = 4 pulse at "A" will reach to "B" and pulse at "B" will reach to "A".
This means that the graph is contrary, the only one that fulfills this is the graph (e).
A 5 cm spring is suspended with a mass of 1 g attached to it which extends the spring by 3.2 cm. The same spring is placed on a frictionless flat surface and charged beads are attached to each end of the spring. With the charged beads attached to the spring, the spring's extension is 0.01 m. What are the charges, in micro-Coulombs, of the beads?
Answers
First, we need to find the spring constant
Force of gravity = force of tension from spring
mg = kx
(1x10^-3)(9.8) = k (3.2x10^-2)
k = .30625
Now we can look at the other situation
Since the spring was moved 0.01 meters, we can find the force
F = kx = (.01)(.30625) = .0030625 N
Now we can set the electric force equal to the force of the beads
kq^2/r^2 = .0030625 N
q = 292 microCoulombs
If a car has a momentum of 2315Ns and its mass is 382kg, how fast is it moving?
Answers
ANSWER:
6.06 m/s
STEP-BY-STEP EXPLANATION:
Given:
Momentum = 2315 N*s
Mass = 382 kg
We can calculate the speed as follows:
[tex]\begin{gathered} p=m\cdot v \\ v=\frac{p}{m} \\ \text{ we replacing} \\ v=\frac{2315}{382} \\ v=6.06\text{ m/s} \end{gathered}[/tex]It moves at a speed of 6.06 m/s
Using an electric current, you can split liquid water to form two new substances, hydrogen and oxygen gases. Is this a change in state. Explain your answer.
Answers
This process (called electrolysis) is not have a change of state. This comes from the fact that the substance (in this case water) does not keep its identity during the change, this means that we don't end up with the same substance; rather we have two new ones, hydrogen and oxygen.
nd in Atlanta you decide to drive around the city. You turn a corner and are driving up a steep hill. Suddenly, a small boy runs out on the street chasing a ball. You slam on the brakes and skid to a stop leaving a 50-foot-long skid mark on the street. The boy calmly walks away but a policemen watching from the sidewalk walks over and gives you a speeding ticket. He points out that the speed limit on this street is 25mph. After you recover your wits, you begin to examine the situation. You determine that the street makes an angle of 25◦with the horizontal and that the coefficient of static friction between your tires and the street is0.80. You also find that the coefficient of kinetic friction between your tires and the street is 0.60. Your car’s information book tells you that the mass of your car is 1600 kg. You weigh 140 lbs. Will you fight the ticket
Answers
skid = 50 ft
Speed limit = 25 mph
angle = 25°
friction coefficient = 0.80
mass = 1600 kg
weight = 140 lbs
A Hydrogen atom is a low density hot gas will give out what type of spectrum?A. A uniform spectrum containing all colorsB. A series of emission lines with equal spaces between the colorsC. A series of emission lines spaced in mathematical sequenceD.a uniform spectrum crossed by numerous dark absorption lines
Answers
The emission of photons takes place when an electron from higher energy orbitals jumps to a lower energy orbital.
Therefore the light emitted will correspond to the energy difference between the orbitals.
When the atom emits the photons, they will have energy equal to the energy difference between the orbitals of the Hydrogen. Therefore the spectrum obtained by the hydrogen gas will contain only those lines which correspond to the energy difference of the orbitals.
Therefore the hydrogen will emit a spectrum that contains a series of emission lines spaced in a mathematical sequence.
Therefore the correct answer is option C.
Which of the following terms represents the number of waves passing a given point each second?Frequency⊝Wavelength⊝Amplitude⊝Velocity⊝CLEAR ALL
Answers
Frequency is defined as number of waves or vibration per unit time.
Therefore, option (a), frequency is the number of waves passing a given point each second, is the correct choice.
Solve: What work is done when 3.0 C is moved through an electric potential difference of 1.5 V?1) 0.5 J2) 2.0 J3) 4.0 J4) 4.5 J
Answers
We know that the work done in an electric potential difference is
[tex]\begin{gathered} W=V\cdot Q \\ W=1.5V\cdot3.0C \\ W=4.5J \end{gathered}[/tex]Therefore, the work done is 4.5 J.A 2000 kg car is stopped by applying a braking force of 5000 newtons.
Determine the acceleration caused by this braking force.
Answers
A 2000 kg car is stopped by applying a braking force of 5000 newtons. The acceleration caused by this braking force is (a)=2.5 m/s²
What is acceleration?When a object start with a velocity and ends with different velocity, so the change in velocity in a given time is called the acceleration of the object. It is a vector quantity. It can be measured in m/s².
How can we calculate the acceleration?To calculate the acceleration we are using the formula here is ,
F=ma
Here we are given by the question is,
F= The amount of force applied on the car. = 5000N.
m= The mass of the car. = 2000kg
We have to calculate the change in acceleration = a m/s².
Now we put the values in above equation we get,
F=ma
Or, a= F/m
Or, a=5000/2000
Or, a=2.5 m/s².
Now from the above calculation we can say that, The acceleration caused by this braking force is (a)=2.5 m/s².
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Choose all the answers that apply.Asteroids:only orbit planetsonly orbit the sunare made of frozen gas and icetake millions of years to orbit the sun sometimes come very close to Earth
Answers
ANSWER:
5th option: sometimes come very close to Earth
STEP-BY-STEP EXPLANATION:
Asteroids are small rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller.
Therefore, of the options the only totally true option is "sometimes come very close to Earth"
So the correct answer is 5th option: sometimes come very close to Earth
Does scarcity effect everyone?
Answers
Answer: Scarcity affects society in every way. First and foremost, scarcity affects the way that individuals make choices. Time and money are two examples of scarce resources that we make choices with every day.
How many cubic inches are there in 3.25 yd3?Express the volume in cubic inches to three significant figures.What is the mass in grams of 16.86 mL of acetone?Express your answer to four significant figures and include the appropriate units.What is the volume in milliliters of 7.06 g of acetone?Express your answer to three significant figures and include the appropriate units.
Answers
Answer:
[tex]\text{ 3.25 yd}^3=151,632in^3[/tex]Explanation: We need to convert cubic-yards into cubic inches, this can be simply done as follows:
[tex]\frac{46656\text{ Cubic inches}}{1\text{ Cubic Yard}}^{}[/tex]Therefore we have:
[tex]\begin{gathered} 3.25\text{ Cubic yards }\times\text{ }\frac{46656\text{ Cubic Inches}}{1\text{ Cubic Yard}}=151,632\text{ Cubic Inches} \\ \therefore\rightarrow \\ \text{ 3.25 yd}^3=151,632in^3 \end{gathered}[/tex]I need help with the following question:
USING THE FOLLOWING CONVERSION FACTOR:
Conversions Longitude:
1 degree= 52.505 miles
1 minute= 4620.5 feet
Conversions for Latitude:
1 degree= 69.005 miles
1 minute= 6072.5 feet
How Do I convert these coordinates into feet?
The length of side A (40° 51.485' N, 74° 12.080' W & 40° 51.485' N, 74° 11.883' W) = ------------- ft
The length of side B (40° 51.485' N, 74° 12.080' W & 40° 51.800' N, 74° 11.883' W) = ----------- ft
Answers
The length of the side A is 1,13,25,866.44 ft N, 2,70,34,989.4 ft W
The length of the side B is 1,13,25,866.44 ft N, 2,70,34,989.4 ft W
Length is the measurement of anything from end to end.
Conversions Longitude:
Longitude is the angular distance of a location east or west of the meridian in Greenwich, England, or west of the standard meridian of a celestial object.
1 degree= 52.505 miles
1 minute= 4620.5 feet
Conversions for Latitude:
Latitude is the angular distance of a location north or south of the Earth's equator.
1 degree= 69.005 miles
1 minute= 6072.5 feet
Also 1 mile = 5280 feet
The length of side A (40° 51.485' N, 74° 12.080' W)
40° 51.485' N = 40 * 52.505 * 5280 + 51.485 * 4620.5
40° 51.485' N = 1,10,88,000 + 2,37,866.44
40° 51.485' N = 1,13,25,866.44 feet.
74° 12.080' W = 74 * 69.005 * 5280 + 12.080 * 6072.5
74° 12.080' W = 2,69,61,633.6 + 73,355.8
74° 12.080' W = 2,70,34,989.4 feet
The length of side B (40° 51.485' N, 74° 12.080' W)
40° 51.485' N = 1,13,25,866.44 feet.
74° 12.080' W = 2,70,34,989.4 feet.
Side A = Side B = 1,13,25,866.44 ft N, 2,70,34,989.4 ft W.
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On a fishing trip Justin rides in a boat 12 km south. The fish aren't biting so they go 4 km west. They then follow a school of fish 1 km north. What is his total displacement?
Answers
ANSWER:
The displacement is 11.7 km
STEP-BY-STEP EXPLANATION:
The displacement is the vector sum from the start point to the end point. Vector addition is applying the formula of the distance between two points.. We will use this formula:
[tex]d=\sqrt[]{(x_2-x^{^{}}_1)^2+(y_2-y_1)^2^{}}[/tex]To better understand the exercise, we will draw a picture of the situation, it would look like this:
Replacing the points (-4, -11) and (0, 0)
[tex]\begin{gathered} d=\sqrt[]{(-4-0^{}^{}_{})^2+(-11_{}-0_{})^2} \\ d=\sqrt[]{16+121^{}} \\ d=\sqrt[]{137} \\ d=11.7 \end{gathered}[/tex]Calculate the height of an image in a converging lens with a height of 6.1 cm, an image location of 6.2 cm, and a distance of 3.6 cm for the object's placement from the lens. Final answer will have 2 decimal places and might not follow sig fig rules.
Answers
the formula we will use is
1/f = 1/p + 1/q
where f is = focal length
p is the distance away (distance from the lens to the object)
and q is the image distance
An unwary football player collides head-on with a padded goalpost while running at 7.5 m/s and comes to a full stop after compressing the padding and his body by 0.27 m. Take the direction of the player’s initial velocity as positive.1.assuming constant acceleration calculate the his acceleration during the collision in meters per second squared.2 how long does the collision last in seconds.
Answers
Answers:
1. a = -104.16 m/s²
2. t = 0.072
Explanation:
To find the acceleration, we will use the following equation:
[tex]v^2_f=v^2_i+2ax[/tex]where vf is the final velocity, vi is the initial velocity, a is the acceleration and x is the distance. So, replacing vf by 0 m/s, vi by 7.5 m/s, and x by 0.27m, we get:
[tex]\begin{gathered} 0^2=7.5^2+2a(0.27) \\ 0=56.25+0.54a \end{gathered}[/tex]Then, solving for a, we get:
[tex]\begin{gathered} 0-56.25=56.25+0.54a-56.25 \\ -56.25=0.54a \\ \frac{-56.25}{0.54}=\frac{0.54a}{0.54} \\ -104.16m/s^2=a \end{gathered}[/tex]Therefore, the acceleration during the collision is -104.16 m/s²
Then, to calculate how long the collision last, we will use the following equation:
[tex]v_f=v_i+at[/tex]So, replacing the values and solving for t, we get:
[tex]\begin{gathered} 0=7.5-104.16t \\ 104.15t=7.5 \\ t=\frac{7.5}{104.15}=0.072s \end{gathered}[/tex]Therefore, the collision last 0.072 seconds
Shown here are astronomical objects located at different distances from earth. rank the objects based on their distances from earth, from farthest to nearest.
- star on far side of Andromeda Galaxy
- star on near side of Andromeda Galaxy
- star on far side of Milky Way Galaxy
- star near center of Milky Way Galaxy
- Orion Nebula
- Alpha Centauri
- Pluto- The Sun
Answers
The distance of astronomical objects is measure very carefully. These are having a different unit. This is the astronomical unit. The distances are very huge.
The distance between objects in space is vast and very difficult to calculate. These are learned under solar system mathematics. The values for these distances are cumbersome for astronomers and scientists to manipulate. Therefore, scientists use a unit of measurement called an astronomical unit.
Let us understand the distances first.
To know the distance of stars in Andromeda Galaxy, we should first know the distance of Andromeda Galaxy. The distance of Andromeda Galaxy from Earth is 2.5 million light years away. The astronomical unit used is the light years.
Thus, from this we can conclude that,
The star near to Andromeda Galaxy must be at a distance of 2.5 million light years away.The star far side from Andromeda Galaxy will be more than 2.5 million light years away.Now to know about the stars in Milky Way Galaxy, the distance of milky way galaxy from Earth is approximately 9 light years away.
So,
The star far from Milky Way Galaxy should be more than 9 light years away from Earth.The star near to the Milky Way Galaxy should be close to 9 light years away from Earth.Orion Nebula is 1,344 light years away.Alpha Centauri is approximately 4.3 light years away from the Earth.The Pluto is approximately 5 billion km away from the Earth.The Sun is approximately 148 million km away from the Earth.Thus, from this we can conclude that,
The farthest is the star on far side of Andromeda Galaxy, then the star on near side of Andromeda Galaxy, then comes the star on far side of Milky Way Galaxy, then the star near center of Milky Way Galaxy, then it is the Alpha Centauri, then the Orion Nebula and then it is the Pluto with the Sun being the nearest one.
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Which one of the pulley systems below has the best force advantage?Select one:a. Pulley Ib. Pulley IIc. Pulley IIId. The force advantage is the same.
Answers
a. Pulley I
Explanation
A pulley system is a collection of one or more wheels which are used with a. rope or chain to make it easier to lift things, The main advantage in the use of pulleys is that the effort becomes less as compared to the normal lifting of the weights
the ideal mechanical advantage is equal to the number of rope segments pulling up on the object. The more rope segments that are helping to do the lifting work, the less force that is needed for the job.
so
Step 1
let's check the number of pulleys on each system
so, the firs system has the more rope segements pulling up (4)
therefore, the answer is
a. Pulley I
I hope this helps you
A student pushes a baseball of m = 0.13 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.18 meters from its original equilibrium point. The spring constant of the spring is k = 970 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring.
A. What is the maximum height, h, in meters, that the ball reaches above the equilibrium point?
B. What is the ball’s velocity, in meters per second, at half of the maximum height relative to the equilibrium point?
Answers
The maximum height reached by the baseball above the equilibrium point is 12.14 m.
The ball’s velocity, in meters per second, at half of the maximum height relative to the equilibrium point is 458.8 m/s.
What is the maximum height attained by the ball?The maximum height reached by the ball is determined as follows:
Data given:
compression of the spring is d = 0.18 m.mass of the baseball is m = 0.13 kgthe spring constant, K = 970 N/mThe gravitational potential energy at the compressed position is zero.
Based on the law of conservation of energy, the total energy of the system is conserved.
Let the final height from the bottom be h
m * g* h = ¹/₂ * K * d²
h = (k * d²) / (2 * m * g)
h = 970 * 0.18² / (2 * 0.13 * 9.81)
h = 12.32 m
Height above the equilibrium point = 12.32 - 0.18
Height above the equilibrium point = 12.14 m
Velocity is calculated1 as follows:
Half of the maximum height relative to the equilibrium point = 12.14/2 + (0.18) = 6.25 m
¹/₂ * m * v² = ¹/₂ * K * d²
m * v² = K * d²
v = √(K * d² / m)
v = √(970 * 6.25² / 0.13)
v = 458.8 m/s
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